(x-3)(2x+4)=0

Solution for (x-3)(2x+4)=0 equation:

Simplifying
(x + -3)(2x + 4) = 0

Reorder the terms:
(-3 + x)(2x + 4) = 0

Reorder the terms:
(-3 + x)(4 + 2x) = 0

Multiply (-3 + x) * (4 + 2x)
(-3(4 + 2x) + x(4 + 2x)) = 0
((4 * -3 + 2x * -3) + x(4 + 2x)) = 0
((-12 + -6x) + x(4 + 2x)) = 0
(-12 + -6x + (4 * x + 2x * x)) = 0
(-12 + -6x + (4x + 2x2)) = 0

Combine like terms: -6x + 4x = -2x
(-12 + -2x + 2x2) = 0

Solving
-12 + -2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1x + x2) = 0

Factor a trinomial.
2((-2 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2, 3}